Exam 3: Radian Measure and the Unit Circle

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of . -Find cot ϴ.

Solve the problem. -Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 38°, find the length of OV accurate to four decimal places.

$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$ -cot s = 0.6921

Solve the problem. -A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, $\theta = 44 ^ { \circ }$ and the radius, $r = 148$ meters. Round to the nearest whole number.

Convert the degree measure to radians, correct to four decimal places. Use $\text { Use } 3.1416 \text { for } \pi \text {. }$ -16.84°

Solve the problem. -A pulley with a diameter of 26 inches is driven by a belt which is moving 859 ft/min. To the nearest unit, how many revolutions per minute are made by the pulley?

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City A, 34° N and City B, 37° N. (Round to the nearest kilometer.)

Solve the problem. -Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 45°, find the exact length of OV.

$\text { Use the formula } \omega = \frac { \theta } { t } \text { to find the value of the missing variable. Give an exact answer unless otherwise indicated. }$ -Ɯ = 1.0775 radians per min, ϴ = 10.77 radians (Round to four decimal places when necessary.)

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \tan \mathrm { s } = - \frac { \sqrt { 3 } } { 3 }$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 4 }$

Solve the problem. -Suppose the tip of the minute hand of a clock is 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Solve the problem. -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 13 seconds a central angle of $\frac { 1 } { 5 }$ radian has been covered, what is the angular speed of the ball?

Solve the problem. -Find the radius of a circle in which a central angle of $\frac { \pi } { 3 }$ radian determines a sector of area 93 square meters. Round to the nearest hundredth.

Solve the problem. -Two pulleys of diameters $6 \mathrm {~m}$ and $3 \mathrm {~m}$ are connected by a belt. The larger pulley rotates 42 times per min. Find the angular speed of the smaller pulley.

Solve the problem. -Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 45°, find the exact length of US.

Approximate the length using the formula for arc length. Round to the nearest meter. -A tree 460 m away subtends an angle of 2°. Find the height of the tree.

Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 19.0 \mathrm {~m} , \theta = 20 ^ { \circ }$

Find the exact circular function value. - $\tan \frac { 5 \pi } { 4 }$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, 30°N, are 2234 km apart.